Efficient simulation of binary adsorption isotherms using transition matrix Monte Carlo

Molecular simulations of binary adsorption in porous materials are a useful complement to experimental studies of mixture adsorption. Most molecular simulations of binary adsorption are performed using grand canonical Monte Carlo (GCMC) to independently examine a range of state points of interest. A disadvantage of this approach is that it only yields information at a discrete set of state points; therefore, if a complete isotherm is required for arbitrary conditions, some type of data fitting or interpolation must be used in combination with the GCMC data. We show that the transition matrix Monte Carlo (TMMC) method of Shen and Errington (Shen, V. K.; Errington, J. R. J. Chem.Phys. 2005, 122, 064508) is well-suited to simulation of binary adsorption in porous materials. At the completion of a TMMC simulation, the adsorption isotherm for all possible bulk phase compositions and pressures is available without data fitting or interpolation. It is also straightforward to use results from TMMC to compute derivatives of the isotherm such as the mixture thermodynamic correction factors, partial differential ln f(i)/partial differential ln c(j), again without data fitting or interpolation. This approach should be useful in contexts where information on the full adsorption isotherm is needed, such as the design of adsorption- or membrane-based separations.     

Grand canonical monte carlo simulation study of water adsorption in silicalite at 300 K

This molecular simulation work focuses on the adsorption of water in a priori hydrophobic silicalite-1, a microporous ordered silica. The water-water interactions are described with the SPC model, while water-silica interactions are calculated in the framework of the PN-TrAZ model. The water adsorption isotherm at 300 K, the configurational energies, and the isosteric heat of adsorption are calculated by the grand canonical Monte Carlo (GCMC) simulation method. The thermodynamic integration scheme allows one to calculate the grand potential along the adsorption isotherm. The adsorption results are compared with experiments, showing only qualitative agreement. Indeed, the simulations do not reproduce the expected hydrophobicity of silicalite (Eroshenko, V.; Regis, R.-C.; Soulard, M.; Patarin, J. C. R. Phys. 2002, 3, 111). This indicates that common models used to describe confined polar molecules are far from being operative. In this work, it is shown, on the basis of periodic ab initio calculations, that confined water molecules in silicalite have a dipole value roughly 10% smaller than that in the bulk liquid phase, indicating that the environment felt by a confined water molecule in silicalite pores is not equivalent to that in the bulk liquid. This suggests that effective intermolecular potentials parametrized for bulk water are inefficient to describe ultraconfined water molecules. Reducing the SPC water dipole moment by 5% (i.e., decreasing water partial charges in magnitude) in GCMC calculations does allow reproducing the experimental water/silicalite isotherm at 300 K.     

Adsorption integral equation via complex approximation with constraints: kernel of general form

For the monolayer adsorption on a homogeneous surface, including arbitrary range lateral interactions, the isotherm can be written as a power series of the Langmuir isotherm. If this isotherm is used as the kernel in the adsorption integral equation, this integral equation can be solved in an analytical form. Because the global isotherm is usually known as a set of experimental values, the use of a numerical method is inevitable. A new numerical method for solving the adsorption integral equation with a kernel of general form is developed. It is based on recent results concerning the structure of the local isotherm and on the ideas of complex approximation with constraints, and allows reduction of the problem under consideration to a linear‐quadratic programming problem. Results of numerical experiments are presented. The method can be useful for the evaluation of the adsorption energy distribution from experimental data. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1058–1066, 2001     

Investigation of activated carbon surface heterogeneity by argon and nitrogen low-pressure quasi-equilibrium volumetry

Surface heterogeneity can be assessed by adsorption of different gaseous probes on solid materials. In the present study, four types of activated carbons were analyzed by classical N2 Brunauer-Emmett-Teller (BET) measurements and by low-pressure quasi-equilibrium volumetry (LPQEV) (Villieras, F.; Michot, L. J.; Bardot, F.; Cases, J. M.; Francois, M.; Rudzinski, W. Langmuir 1997, 13, 1104). Three methods of data evaluation were applied: (a) the Frenkel-Halsey-Hill method for estimation of fractal dimensions from BET data, (b) the Horwath-Kawazoe method to calculate the pore size distribution from LPQEV Ar and N2 adsorption isotherms, and (c) the derivative isotherm summation (DIS) method to describe the solid's surface heterogeneity by a concept of local derivative isotherms. Similar Ar and N2 adsorption energy distributions were obtained on all carbons, which indicates the presence of mainly nonpolar surfaces. When adsorption was described by the van der Waals equation, the ratio between the interaction energy of different energetic sites with argon and nitrogen was 0.88. This value corresponded very well with a slope obtained when Ar and N2 positions of local isotherms by the DIS method were compared. This relationship has an important impact because it enables one to constrain the modeling of local isotherms. This study, besides the surface information, showed large possibilities of the DIS method for the surface analysis not only in terms of solid heterogeneity characterization but also in terms of polarity assessment.     

Modeling of adsorption on nongraphitized carbon surface: GCMC simulation studies and comparison with experimental data

We model nongraphitized carbon black surfaces and investigate adsorption of argon on these surfaces by using the grand canonical Monte Carlo simulation. In this model, the nongraphitized surface is modeled as a stack of graphene layers with some carbon atoms of the top graphene layer being randomly removed. The percentage of the surface carbon atoms being removed and the effective size of the defect (created by the removal) are the key parameters to characterize the nongraphitized surface. The patterns of adsorption isotherm and isosteric heat are particularly studied, as a function of these surface parameters as well as pressure and temperature. It is shown that the adsorption isotherm shows a steplike behavior on a perfect graphite surface and becomes smoother on nongraphitized surfaces. Regarding the isosteric heat versus loading, we observe for the case of graphitized thermal carbon black the increase of heat in the submonolayer coverage and then a sharp decline in the heat when the second layer is starting to form, beyond which it increases slightly. On the other hand, the isosteric heat versus loading for a highly nongraphitized surface shows a general decline with respect to loading, which is due to the energetic heterogeneity of the surface. It is only when the fluid-fluid interaction is greater than the surface energetic factor that we see a minimum-maximum in the isosteric heat versus loading. These simulation results of isosteric heat agree well with the experimental results of graphitization of Spheron 6 (Polley, M. H.; Schaeffer, W. D.; Smith, W. R. J. Phys. Chem. 1953, 57, 469; Beebe, R. A.; Young, D. M. J. Phys. Chem. 1954, 58, 93). Adsorption isotherms and isosteric heat in pores whose walls have defects are also studied from the simulation, and the pattern of isotherm and isosteric heat could be used to identify the fingerprint of the surface.     

VBSM: a solvation model based on valence bond theory

A new solvation model, called VBSM, is presented. The model combines valence bond (VB) theory with parameters determined for the SM6 solvation model (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). VBSM, like SM6, is based on the generalized Born (GB) approximation for bulk electrostatics and atomic surface tensions to account for cavitation, dispersion, and solvent structure (CDS). The solvation free energy of VBSM includes (i) a self-consistent polarization term obtained by using VB atomic charges in a GB reaction field with a VB self-consistent field procedure that minimizes the total energy of the system with respect to the valence bond orbitals and (ii) a geometry-dependent CDS term to account for deviations from bulk-electrostatic solvation. Test calculations for a few systems show that the liquid-phase partial atomic charges obtained by VBSM are in good agreement with liquid-phase charges obtained by charge model CM4 (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theo. Comp. 2005, 1, 1133-1152). Free energies of solvation are calculated for two prototype test cases, namely, for the degenerate S(N)2 reaction of Cl(-) with CH(3)Cl in water and for a Menshutkin reaction in water. These calculations show that the VBSM method provides a practical alternative to single-configuration self-consistent field theory for solvent effects in molecules and chemical reactions.     

Modeling of adsorption in hydrophobic interaction chromatography systems using a preferential interaction quadratic isotherm

A preferential interaction quadratic isotherm model for hydrophobic interaction chromatographic systems is presented in this paper. In this isotherm, the nonlinear effect of salt on the capacity factor is described using the preferential interaction model developed by Perkins et al. [J. Chromatogr. A, 766 (1997) 1]. This is then coupled with a quadratic nonlinear isotherm to describe nonlinear adsorption behavior at high solute concentrations. The resulting preferential interaction quadratic isotherm is examined for its ability to describe solute adsorption behavior under both linear and nonlinear conditions over a wide range of salt concentrations in HIC systems. The results indicate that this isotherm is well suited for predicting nonlinear adsorption behavior in HIC systems for both proteins and low-molecular mass HIC displacers.     

Gyroscopic effect in low-energy classical capture of a rotating quadrupolar diatom by an ion

The low-energy capture of homonuclear diatoms by ions is due mainly to the long-range part of the interpartner potential with leading terms that correspond to charge-quadrupole interaction and charge-induced dipole interaction. The capture dynamics is described by the perturbed-rotor adiabatic potentials and the Coriolis interaction between manifold of states that belong to a given value of the intrinsic angular momentum. When the latter is large enough, it can noticeably affect the capture cross section calculated in the adiabatic channel approximation due to the gyroscopic property of a rotating diatom. This paper presents the low-energy (low-temperature) state-selected partial and mean capture cross sections (rate coefficients) for the charge-quadrupole interaction that include the gyroscopic effect (decoupling of intrinsic angular momentum from the collision axis), quantum correction for the diatom rotation, and the correction for the charge-induced dipole interaction. These results complement recent studies on the gyroscopic effect in the quantum regime of diatom-ion capture (Dashevskaya, E. I.; Litvin, I.; Nikitin, E. E.; Troe, J. J. Chem. Phys. 2004, 120, 9989-9997).     

国产硅藻土吸附尿激酶机理的研究

在常温下, 尿激酶在浙江土和吉林土表面的吸附等温线分别为V型和II型; 焙烧后两者皆转为III型。吸附等温线类型与硅藻土表面结构、孔结构、表面ζ电位有关。在400℃焙烧的硅藻土等电点值最低, 吸附量最大; 改性后, 吸附量也发生改变。本文还测定了尿激酶在硅藻土表面的吸附形态, 其吸附等温线方程符合0/(1-0)=(Kc)^1/β, 并讨论了平衡常数K和尿激酶吸附功能链段数β随温度的变化。     

Ab initio equation of state of an organic molecular crystal: 1,1-diamino-2,2-dinitroethylene

A complete equation of state for the molecular crystal 1,1-diamino-2,2-dinitroethylene has been calculated from first principles for temperatures between 0 and 400 K, and for specific volumes from 61 to 83 cm3/mol, corresponding to relative volumes from 0.78 to 1.06. The calculated 300 K isotherm agrees very well with the experimentally measured pressure-volume relation reported by Peiris et al. (Peiris, S. M.; Wong, C. P.; Zerilli, F. J. J. Chem. Phys. 2004, 120, 8060). The volumetric thermal expansion coefficient is calculated to be 140 ppm/K at 300 K and atmospheric pressure and varies considerably with specific volume as well as temperature. The Grüneisen parameter varies significantly with temperature, but its variation with specific volume is small. The calculated specific heat (160 J/mol/K at 300 K and atmospheric pressure) has only a very small dependence on specific volume.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

Electron magnetic resonance and density functional theory study of room temperature X-irradiated β-D-fructose single crystals

Stable free radical formation in fructose single crystals X-irradiated at room temperature was investigated using Q-band electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR), and ENDOR induced EPR (EIE) techniques. ENDOR angular variations in the three main crystallographic planes allowed an unambiguous determination of 12 proton HFC tensors. From the EIE studies, these hyperfine interactions were assigned to six different radical species, labeled F1-F6. Two of the radicals (F1 and F2) were studied previously by Vanhaelewyn et al. [Vanhaelewyn, G. C. A. M.; Pauwels, E.; Callens, F. J.; Waroquier, M.; Sagstuen, E.; Matthys, P. J. Phys. Chem. A 2006, 110, 2147.] and Tarpan et al. [Tarpan, M. A.; Vrielinck, H.; De Cooman, H.; Callens, F. J. J. Phys. Chem. A 2009, 113, 7994.]. The other four radicals are reported here for the first time and periodic density functional theory (DFT) calculations were used to aid their structural identification. For the radical F3 a C3 carbon centered radical with a carbonyl group at the C4 position is proposed. The close similarity in HFC tensors suggests that F4 and F5 originate from the same type of radical stabilized in two slightly different conformations. For these radicals a C2 carbon centered radical model with a carbonyl group situated at the C3 position is proposed. A rather exotic C2 centered radical model is proposed for F6.     

Determinants of cyanuric acid and melamine assembly in water

While the recognition of cyanuric acid (CA) by melamine (M) and their derivatives has been known to occur in both water and organic solvents for some time, analysis of CA/M assembly in water has not been reported (Ranganathan, A.; Pedireddi, V. R.; Rao, C. N. R. J. Am. Chem. Soc.1999, 121, 1752-1753; Mathias, J. P.; Simanek, E. E.; Seto, C. T.; Whitesides, G. M. Macromol. Symp.1994, 77, 157-166; Zerkowski, J. A.; MacDonald, J. C.; Seto, C. T.; Wierda, D. A.; Whitesides, G. M. J. Am. Chem. Soc.1994, 116, 2382-2391; Mathias, J. P.; Seto, C. T.; Whitesides, G. M. Polym. Prepr.1993, 34, 92-93; Seto, C. T.; Whitesides, G. M. J. Am. Chem. Soc.1993, 115, 905-916; Zerkowski, J. A.; Seto, C. T.; Whitesides, G. M. J. Am. Chem. Soc.1992, 114, 5473-5475; Seto, C. T.; Whitesides, G. M. J. Am. Chem. Soc.1990, 112, 6409-6411; Wang, Y.; Wei, B.; Wang, Q. J. Chem. Cryst.1990, 20, 79-84; ten Cate, M. G. J.; Huskens, J.; Crego-Calama, M.; Reinhoudt, D. N. Chem.-Eur. J.2004, 10, 3632-3639). We have examined assembly of CA/M, as well as assembly of soluble trivalent CA and M derivatives (TCA/TM), in aqueous solvent, using a combination of solution phase NMR, isothermal titration and differential scanning calorimetry (ITC/DSC), cryo-transmission electron microscopy (cryo-TEM), and synthetic chemistry. While the parent heterocycles coprecipitate in water, the trivalent system displays more controlled and cooperative assembly that occurs at lower concentrations than the parent and yields a stable nanoparticle suspension. The assembly of both parent and trivalent systems is rigorously 1:1 and proceeds as an exothermic, proton-transfer coupled process in neutral pH water. Though CA and M are considered canonical hydrogen-bonding motifs in organic solvents, we find that their assembly in water is driven in large part by enthalpically favorable surface-area burial, similar to what is observed with nucleic acid recognition. There are currently few synthetic systems capable of robust molecular recognition in water that do not rely on native recognition motifs, possibly due to an incomplete understanding of recognition processes in water. This study establishes a detailed conceptual framework for considering CA/M heterocycle recognition in water which enables the future design of molecular recognition systems that function in water.     

Direct measurement by laser flash photolysis of intraprotein electron transfer in a rat neuronal nitric oxide synthase

Intraprotein interdomain electron transfer (IET) from flavin mononucleotide (FMN) to heme is essential in nitric oxide (NO) synthesis by NO synthase (NOS). Our previous laser flash photolysis studies have provided a direct determination of the kinetics of IET between the FMN and heme domains in truncated oxyFMN constructs of rat neuronal NOS (nNOS) and murine inducible NOS (iNOS), in which only the oxygenase and FMN domains along with the calmodulin (CaM) binding site are present [Feng, C. J.; Tollin, G.; Holliday, M. A.; Thomas, C.; Salerno, J. C.; Enemark, J. H.; Ghosh, D. K. Biochemistry 2006, 45, 6354-6362. Feng, C. J.; Thomas, C.; Holliday, M. A.; Tollin, G.; Salerno, J. C.; Ghosh, D. K.; Enemark, J. H. J. Am. Chem. Soc. 2006, 128, 3808-3811]. Here, we report the kinetics of IET between the FMN and heme domains in a rat nNOS holoenzyme in the presence and absence of added CaM using laser flash photolysis of CO dissociation in comparative studies on partially reduced NOS and a single domain NOS oxygenase construct. The IET rate constant in the presence of CaM is 36 s-1, whereas no IET was observed in the absence of CaM. The kinetics reported here are about an order of magnitude slower than the kinetics in a rat nNOS oxyFMN construct with added CaM (262 s-1). We attribute the slower IET between FMN and heme in the holoenzyme to the additional step of dissociation of the FMN domain from the reductase complex before reassociation with the oxygenase domain to form the electron-transfer competent output state complex. This work provides the first direct measurement of CaM-controlled electron transfer between catalytically significant redox couples of FMN and heme in a nNOS holoenzyme.     

Rate constants and H atom branching ratios of the gas-phase reactions of methylidyne CH(X2Pi) radical with a series of alkanes

The reactions of the CH radical with several alkanes were studied, at room temperature, in a low-pressure fast-flow reactor. CH(X2Pi, v = 0) radicals were obtained from the reaction of CHBr(3) with potassium atoms. The overall rate constants at 300 K are (0.76 +/- 0.20) x 10(-10) [Fleurat-Lessard, P.; Rayez, J. C.; Bergeat, A.; Loison, J. C. Chem. Phys. 2002, 279, 87],1 (1.60 +/- 0.60) x 10(-10)[Galland, N.; Caralp, F.; Hannachi, Y.; Bergeat, A.; Loison, J.-C. J. Phys. Chem. A 2003, 107, 5419],2 (2.20 +/- 0.80) x 10(-10), (2.80 +/- 0.80) x 10(-10), (3.20 +/- 0.80) x 10(-10), (3.30 +/- 0.60) x 10(-10), and (3.60 +/- 0.80) x 10(-10) cm3 molecule(-1) s(-1), (errors refer to +/-2sigma) for methane, ethane, propane, n-butane, n-pentane, neo-pentane, and n-hexane respectively. The experimental overall rate constants correspond to those obtained using a simple classical capture theory. Absolute atomic hydrogen production was determined by V.U.V. resonance fluorescence, with H production from the CH + CH4 reaction being used as a reference. Observed H branching ratios were for CH4, 1.00[Fleurat-Lessard, P.; Rayez, J. C.; Bergeat, A.; Loison, J. C. Chem. Phys. 2002, 279, 87];1 C(2)H(6), 0.22 +/- 0.08 [Galland, N.; Caralp, F.; Hannachi, Y.; Bergeat, A.; Loison, J.-C. J. Phys. Chem. A 2003, 107, 5419];2 C(3)H(8), 0.19 +/- 0.07; C(4)H(10) (n-butane), 0.14 +/- 0.06; C(5)H(12) (n-pentane), 0.52 +/- 0.08; C(5)H(12) (neo-pentane), 0.51 +/- 0.08; C(5)H(12) (iso-pentane), 0.12 +/- 0.06; C(6)H(14) (n-hexane), 0.06 +/- 0.04.     

Adsorption-desorption isotherm hysteresis of beta-lactoglobulin A with a weakly hydrophobic surface.

Adsorption-desorption isotherms of bovine beta-lactoglobulin A (beta-lact A) on a weakly hydrophobic stationary phase (C1-ether) were measured by frontal analysis. The adsorption isotherms obtained at different pH were found to be dramatically different in shape, column capacity and desorption reversibility. At pH 4.5, an S-shaped adsorption isotherm was observed whereas at pH 6.0 a Langmuir isotherm was found. In addition, the desorption isotherm at pH 6.0 was found to overlap with the adsorption isotherm, and the adsorption-desorption process of beta-lact A under this condition could be characterized by a fully reversible Langmuir model. The desorption isotherm at pH 4.5, however, did not retrace the adsorption isotherm, resulting in hysteresis loops. A higher aggregate (tetramer) of beta-lact A is shown to be in an equilibrium with the beta-lact A protomer (dimer) at pH 4.5 whereas the dimer alone is predominant at pH 6.0. It is further shown that changes in the absorption coefficient between the adsorption and the desorption cycles for the tetramer at pH 4.5 can account for the hysteresis. The results demonstrate that pH can be a sensitive parameter in protein adsorption isotherm behavior and ultimately the behavior of species in preparative-scale chromatography.     

A simple approach for improving the hybrid MMVB force field: application to the photoisomerization of s-cis butadiene

MMVB is a QM/MM hybrid method, consisting of a molecular mechanics force field coupled to a valence bond Heisenberg Hamiltonian parametrized from ab initio CASSCF calculations on several prototype molecules. The Heisenberg Hamiltonian matrix elements Q(ij) and K(ij), whose expressions are partitioned here into a primary contribution and second-order correction terms, are calculated analytically in MMVB. When the original MMVB force field fails to produce potential energy surfaces accurate enough for dynamics calculations, we show that significant improvements can be made by refitting the second-order correction terms for the particular molecule(s) being studied. This "local" reparametrization is based on values of K(ij) extracted (using effective Hamiltonian techniques) from CASSCF calculations on the same molecule(s). The method is demonstrated for the photoisomerization of s-cis butadiene, and we explain how the correction terms that enabled a successful MMVB dynamics study [Garavelli, M.; Bernardi, F.; Olivucci, M.; Bearpark, M. J.; Klein, S.; Robb, M. A. J Phys Chem A 2001, 105, 11496] were refitted.     

A stepwise approximation for modeling of the wall-fluid potential of a mesoscopic pore

A common computational method for the characterization of porous materials is to calculate the adsorption isotherm of fluids in the materials from the pre-assumed wall-fluid potential. If the wall-fluid potential is unknown, the common computational method becomes invalid. In a realistic experiment, however, it is common to know the experimental adsorption isotherm of nitrogen and not to know the wall-fluid potential. Here we propose a stepwise approximation for modeling wall-fluid potential under conditions where only the adsorption isotherm of nitrogen is measured experimentally. Based on the modeled wall-fluid potential, we can characterize the porous materials and predict the adsorption of other adsorbates on the materials. It is expected that the approach would provide a powerful means for the characterization of novel materials under conditions where only the experimental adsorption isotherm is available.